Common Core Learning Standard
Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students will recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures the center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students will recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median, yet be distinguished by their variability. Students will learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry considering the context in which the data were collected. The Mathematical Practices should be evident throughout instruction and connected to the content addressed in this unit. Students should engage in mathematical tasks that provide an opportunity to connect content and practices.
Big Ideas
• Understand that statistics is a way of analyzing number sets into meaningful and quantitative information.
• Interpret and explain statistical measures for given number sets.
• Represent statistical data using visual representations such as tables, charts, and plots.
Essential Concepts
• Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers
•Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
• Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
• Understand that numerical data can be displayed in plots on a number line, including dot plots, histograms, and box plots.
• Summarize numerical data sets in relation to their context, such as by:
• Reporting the number of observations.
• Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
• Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
• Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered
Vocabulary
• Box and Whisker Plot- A diagram that summarizes data using the median, the upper and lowers quartiles, and the extreme values (minimum and maximum). Box and whisker plots are also known as box plots. It is constructed from the five-number summary of the data: Minimum, Q1 (lower quartile), Q2 (median), Q3 (upper quartile), Maximum.
• Frequency- the number of times an item, number, or event occurs in a set of data
• Grouped Frequency Table- The organization of raw data in table form with classes and frequencies
• Histogram- a way of displaying numeric data using horizontal or vertical bars so that the height or length of the bars indicates frequency
• Inter-Quartile Range (IQR)- The difference between the first and third quartiles. (Note that the first quartile and third quartiles are sometimes called upper and lower quartiles.)
• Maximum value- The largest value in a set of data.
• Mean Absolute Deviation- the average distance of each data value from the mean. The MAD is a gauge of “on average” how different the data values are form the mean value.
• Mean- The “average” or “fair share” value for the data. The mean is also the balance point of the corresponding data distribution.
• Measures of Center- The mean and the median are both ways to measure the center for a set of data.
• Measures of Spread- The range and the Mean Absolute Deviation are both common ways to measure the spread for a set of data.
• Median- The value for which half the numbers are larger and half are smaller. If there are two middle numbers, the median is the arithmetic mean of the two middle numbers. Note: The median is a good choice to represent the center of a distribution when the distribution is skewed or outliers are present.
• Minimum value- The smallest value in a set of data.
• Mode- The number that occurs the most often in a list. There can be more than one mode, or no mode.
• Outlier- A value that is very far away from most of the values in a data set.
• Range- A measure of spread for a set of data. To find the range, subtract the smallest value from the largest value in a set of data.
• Stem and Leaf Plot- A graphical method used to represent ordered numerical data. Once the data are ordered, the stem and leaves are determined. Typically the stem is all but the last digit of each data point and the leaf is that last digit.
Content
In this unit students will:
• Analyze data from many different sources such as organized lists, box-plots, bar graphs and stem-and-leaf plots
• Understand that responses to statistical questions may vary
• Understand that data can be described by a single number
• Determine quantitative measures of center (median and/or mean)
• Determine quantitative measures of variability (interquartile range and/or mean absolute deviation)
Skills Needed
• Analyzing patterns and seeing relationships
• Fluency with operations on multi-digit numbers and decimals
number of observations
describing nature of statistic being measured
giving quantitative measures
relating choice of measures and variable to shape of distribution
6.SP.1
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
6.SP.2
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.3
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
6.SP.4
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.5
Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
Table of Contents
Common Core Learning Standard
Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students will recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures the center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students will recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median, yet be distinguished by their variability. Students will learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry considering the context in which the data were collected. The Mathematical Practices should be evident throughout instruction and connected to the content addressed in this unit. Students should engage in mathematical tasks that provide an opportunity to connect content and practices.
Big Ideas
• Understand that statistics is a way of analyzing number sets into meaningful and quantitative information.
• Interpret and explain statistical measures for given number sets.
• Represent statistical data using visual representations such as tables, charts, and plots.
Essential Concepts
• Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers
•Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
• Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
• Understand that numerical data can be displayed in plots on a number line, including dot plots, histograms, and box plots.
• Summarize numerical data sets in relation to their context, such as by:
• Reporting the number of observations.
• Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
• Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
• Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered
Vocabulary
• Box and Whisker Plot- A diagram that summarizes data using the median, the upper and lowers quartiles, and the extreme values (minimum and maximum). Box and whisker plots are also known as box plots. It is constructed from the five-number summary of the data: Minimum, Q1 (lower quartile), Q2 (median), Q3 (upper quartile), Maximum.
• Frequency- the number of times an item, number, or event occurs in a set of data
• Grouped Frequency Table- The organization of raw data in table form with classes and frequencies
• Histogram- a way of displaying numeric data using horizontal or vertical bars so that the height or length of the bars indicates frequency
• Inter-Quartile Range (IQR)- The difference between the first and third quartiles. (Note that the first quartile and third quartiles are sometimes called upper and lower quartiles.)
• Maximum value- The largest value in a set of data.
• Mean Absolute Deviation- the average distance of each data value from the mean. The MAD is a gauge of “on average” how different the data values are form the mean value.
• Mean- The “average” or “fair share” value for the data. The mean is also the balance point of the corresponding data distribution.
• Measures of Center- The mean and the median are both ways to measure the center for a set of data.
• Measures of Spread- The range and the Mean Absolute Deviation are both common ways to measure the spread for a set of data.
• Median- The value for which half the numbers are larger and half are smaller. If there are two middle numbers, the median is the arithmetic mean of the two middle numbers. Note: The median is a good choice to represent the center of a distribution when the distribution is skewed or outliers are present.
• Minimum value- The smallest value in a set of data.
• Mode- The number that occurs the most often in a list. There can be more than one mode, or no mode.
• Outlier- A value that is very far away from most of the values in a data set.
• Range- A measure of spread for a set of data. To find the range, subtract the smallest value from the largest value in a set of data.
• Stem and Leaf Plot- A graphical method used to represent ordered numerical data. Once the data are ordered, the stem and leaves are determined. Typically the stem is all but the last digit of each data point and the leaf is that last digit.
Content
In this unit students will:
• Analyze data from many different sources such as organized lists, box-plots, bar graphs and stem-and-leaf plots
• Understand that responses to statistical questions may vary
• Understand that data can be described by a single number
• Determine quantitative measures of center (median and/or mean)
• Determine quantitative measures of variability (interquartile range and/or mean absolute deviation)
Skills Needed
• Analyzing patterns and seeing relationships
• Fluency with operations on multi-digit numbers and decimals
&
Vocabulary
on
Topic
Lessons
Pages
Resources
Module 1
Understanding & Calculating
6.SP.5c
median
mode
range
Outlier
median
mode
range
CMP3 pages 41 - 44
Biased Questions
578-579
Module 2
Charts, Graphs, and Distributionsincorporate S.P.5 abcd into lessons
center
spread
overall shape
584-587
XP Math Game
XP Math Games
incorporate S.P.5 abcd into lessons
2-2
Independent
6.SP.4
6.SP.5c
Dot Plots
468- 487
578-580
585-587
parts of 592-600
608-612
Inter-quartile range
Module 3
describing nature of statistic being measured
giving quantitative measures
relating choice of measures and variable to shape of distribution
2-2
2-6
2-7
CC-2
CC-1
CC-3
578-583
601-616
608-612
Independent
Unit Assessments
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
6.SP.2
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.3
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
6.SP.4
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.5
Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.